MURORAN INSTITUTE OF TECHNOLOGY A set of electron collision cross sections for CHF 3 Satoru Kawaguchi*, Kohki Satoh and Hidenori Itoh 8th International Conference on Reactive Plasmas 31th Symposium on Plasma Processing 4-7 February 2014, Fukuoka, Japan Division of Information & Electronic Engineering. Graduate School of Muroran Institute of Technology. [email protected] 5. Particle Production and Behavior 5C-AM-O1 C F H Trifluoromethane Contents 1. Introduction 2. Evaluating previously reported sets 3. Estimating the new set 4. Conclusions
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MURORAN INSTITUTE OF TECHNOLOGY
A set of electron collision cross sections
for CHF3
Satoru Kawaguchi*, Kohki Satoh and Hidenori Itoh
8th International Conference on Reactive Plasmas31th Symposium on Plasma Processing4-7 February 2014, Fukuoka, Japan
Division of Information & Electronic Engineering.
Graduate School of Muroran Institute of Technology.
5. Particle Production and Behavior5C-AM-O1
CF
H
Trifluoromethane
� Contents
1. Introduction2. Evaluating previously reported sets3. Estimating the new set 4. Conclusions
MURORAN INSTITUTE OF TECHNOLOGY
Introduction #1(Background)
• CHF3 is an etching gas in substitution for CF4 because of its shorter lifetime in the atmosphere.
Lifetime (yrs.) 500 yrs. Global Warming Potential
CF4 50,000 10,000
CHF3 267 9,800
J. T. Houghton et al.: Climate Change 1995: The Science of Climate Change (Cambridge University Press, Cambridge, 1996)
CF
H
Trifluoromethane
• For effective use of CHF3 gas in a plasma etching, we have to understand the plasma properties in CHF3 gas.
• Computer simulation is a powerful tool for understanding the plasma properties.
• To improve the accuracy of plasma simulation, we have to use the accurate data, such as electron transport coefficients and rate coefficients.
• These coefficients are measured by real experiment, and also calculated with Monte Carlo simulation and Boltzmann equation analysis using a set of electron cross sections.
• To obtain the accurate coefficients, the accurate set of cross sections is required.
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• We evaluate previously reported sets from calculated electron transport coefficients.
Kushner et al. (2000) Bordage et al. (2001) Morgan et al. (2003)Nakamura (2006) Voloshin et al. (2007)
• We estimate the accurate cross section set for CHF3.
• For the accuracy of the calculation, we use Monte Carlo simulation.
To propose an accurate set for CHF3 gas
Introduction #2 (Previous work and Objective)• The sets of cross sections for CHF3 have been reported in following papers.
� Kushner et al. : J. Appl. Phys. 88 (2000) 3231� Bordage et al. : XXV ICPIG Proc. 3 (2001) 253� Morgan et al. : J. Appl. Phys. 90 (2001) 2009� Nakamura : Proc. XVI Int. Conf. Gas Discharges and their Applications 2 (2006) 797� Voloshin et al. : IEEE Trans. Plasma Sci. 35 (2007) 1691
• However, the shape, kind and number of cross sections in previously reported sets are not the same.
• We have to evaluate previously reported cross sections.
� Objective
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Evaluating previously reported sets
MURORAN INSTITUTE OF TECHNOLOGY
Previously reported setsKushner et al. Bordage et al. Morgan et al.
J. Appl. Phys. 88 (2000) 3231 XXV ICPIG, Nagoya, Japan, 33 (2001) 33 J. Phys. D, 90 (2001) 2009
Nakamura Voloshin et al.XVI GD2006, Xi’an, China, 2 (2006) 797 IEEE Trans. Plasma. Sci. 35 (2007) 1691
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10-12
Cro
ss s
ectio
n
[cm2 ]
10-2
10-1
100
101
102
103
Electron energy [eV]
qm
qvibqd
qi
qa×10010
-19
10-18
10-17
10-16
10-15
10-14
10-13
10-12
Cro
ss s
ectio
n
[cm2 ]
10-2
10-1
100
101
102
103
Electron energy [eV]
qm
qvib
qa×100
qd
qi
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10-17
10-16
10-15
10-14
10-13
10-12
Cro
ss s
ectio
n
[cm2 ]
10-2
10-1
100
101
102
103
Electron energy [eV]
qm
qvib
qdqi
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10-15
10-14
10-13
10-12
Cro
ss s
ectio
n
[cm2 ]
10-2
10-1
100
101
102
103
Electron energy [eV]
qm
qvib
qd
qi
qa×100
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10-15
10-14
10-13
10-12
Cro
ss s
ectio
n
[cm2 ]
10-2
10-1
100
101
102
103
Electron energy [eV]
qvib
qm
qdqi
qa×100
• Each of cross section sets consists of qm, qvib, qa, qd and qi, except for Morgan’s set.
• We calculate electron drift velocity, longitudinal diffusion coefficient and effective ionisation coefficient, using these sets and compare calculated parameters with measured data.
MURORAN INSTITUTE OF TECHNOLOGY
Comparison of electron drift velocity
104
105
106
107
108
Ele
ctro
n d
rift v
elo
city
[c
m/s
]
10-1
100
101
102
103
E/N [Td]
Measurements Pulsed experiment (Wang et al. (1999)) Double-shutter method (Nakamura (2006))
This graph shows measured electron drift velocity as a function of E/N.
MURORAN INSTITUTE OF TECHNOLOGY
104
105
106
107
108
Ele
ctro
n d
rift v
elo
city
[c
m/s
]
10-1
100
101
102
103
E/N [Td]
Measurements Pulsed experiment (Wang et al. (1999)) Double-shutter method (Nakamura (2006))
Monte Carlo simulation (MCS) (Wm)
w/ Kushner's set w/ Bordage's set w/ Morgan's set w/ Nakamura's set w/ Voloshin's set
Comparison of electron drift velocity
� The calculated values using Voloshin's set (plotted as ◆) agree well with measured data in a wide range of E/N.
� The other calculated values differ from measured data, particularly at low E/N region.
MURORAN INSTITUTE OF TECHNOLOGY
Comparison of longitudinal diffusion coefficient
1020
2
4
6
810
21
2
4
6
810
22
2
4
6
810
23
Lo
ng
itud
inal
diff
usi
on
co
effic
ien
t ND
L
[cm
-1s-1
]
100
2 3 4 5 6
101
2 3 4 5 6
102
2 3 4 5 6
103
E/N [Td]
Measurement Double-shutter method
(Nakamura (2006))
This graph shows measured longitudinal diffusion coefficient as a function of E/N.
MURORAN INSTITUTE OF TECHNOLOGY
Comparison of longitudinal diffusion coefficient
� The calculated values using Nakamura’s set (plotted as ●) agree well with measured data in a wide range of E/N.
� The other calculated values differ from measured data at low E/N.
1020
2
4
6
810
21
2
4
6
810
22
2
4
6
810
23
Lo
ng
itud
inal
diff
usi
on
co
effic
ien
t ND
L
[cm
-1s-1
]
100
2 3 4 5 6
101
2 3 4 5 6
102
2 3 4 5 6
103
E/N [Td]
Measurement Double-shutter method
(Nakamura (2006))MCS
w/ Kushner's set w/ Bordage's set w/ Morgan's set w/ Nakamura's set w/ Voloshin's set
MURORAN INSTITUTE OF TECHNOLOGY
Comparison of effective ionisation coefficient
200x10-18
150
100
50
0
Effe
ctiv
e io
nis
atio
n c
oef
ficie
nt
(α−η)
/ N
[c
m2 ]
3 4 5 6 7 8 9
102
2 3 4 5 6 7 8 9
103
E/N [Td]
Measurements Pulsed experiment (de Urquijo et al. (1999)) SST experiment (Nakamura (2006))
This graph shows measured effective ionisation coefficient as a function of E/N.
MURORAN INSTITUTE OF TECHNOLOGY
Comparison of effective ionisation coefficient
200x10-18
150
100
50
0
Effe
ctiv
e io
nis
atio
n c
oef
ficie
nt
(α−η)
/ N
[c
m2 ]
3 4 5 6 7 8 9
102
2 3 4 5 6 7 8 9
103
E/N [Td]
Measurements Pulsed experiment (de Urquijo et al. (1999)) SST experiment (Nakamura (2006))
MCS
w/ Kushner's set w/ Bordage's set w/ Morgan's set w/ Nakamura's set w/ Voloshin's set
� The calculated values are close to measured data, but no calculated values agree well with measured data.
MURORAN INSTITUTE OF TECHNOLOGY
Comparison of effective ionisation coefficient
200x10-18
150
100
50
0
Effe
ctiv
e io
nis
atio
n c
oef
ficie
nt
(α−η)
/ N
[c
m2 ]
3 4 5 6 7 8 9
102
2 3 4 5 6 7 8 9
103
E/N [Td]
Measurements Pulsed experiment (de Urquijo et al. (1999)) SST experiment (Nakamura (2006))
MCS
w/ Kushner's set w/ Bordage's set w/ Morgan's set w/ Nakamura's set w/ Voloshin's set
� Electron drift velocityThe calculated values using Voloshin’sset agree well with measured data.
� Longitudinal diffusion coefficientThe calculated values using Nakamura’s set agree well with measured data.
� Effective ionisation coefficientNo calculated values agree well with measured data.
This leads that the accurate set of cross sections for CHF3 needs to be estimated.
� The calculated values are close to measured data, but no calculated values agree well with measured data.
MURORAN INSTITUTE OF TECHNOLOGY
Estimating the new set of cross
sections for CHF3
MURORAN INSTITUTE OF TECHNOLOGY
Estimated set for CHF3
� Momentum transfer qm
� Vibrational excitation qvib(4)
� Electron attachment qa(1)• to be dissociated into F-
� Dissociation qd(5)• to be dissociated into
neutral species
� Dissociative ionisation qi(10)• to be dissociated into
positive ions
This set consists of
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Cro
ss s
ect
ion
[cm2 ]
10-2
10-1
100
101
102
103
Electron energy [eV]
v4
v2
v1v3
qa (1)×100
qm
CF3
CHF2
CF2
CHF
CF
HF+
C+
CHF+
CH+
F+
H+
CF2+
CF+
CHF2+
CF3+qvib (4)
qi (10)
qd (5)
F-
MURORAN INSTITUTE OF TECHNOLOGY
Momentum transfer qm
• qm follows measured data (Cho et al.[1] and Iga et al.[2] ) above 1.5 eV
• Below 1.5 eV, we estimated the shape of qm.
[1] I. Iga et al. : J. Phys. B, 38 (2005) 2319 , [2] H. Cho et al. : J. Phys. B, 43 (2010) 135205
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ectio
n [
cm2 ]
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100
101
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103
Electron energy [eV]
qm Experiment Iga et al. (2005) Cho et al. (2010)
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Vibrational excitation qvib(4) and electron attachment qa(1)
• qvib and qa are taken from Nakamura's set (XVI GD2006, Xi’an, China, 2 (2006) 797)
• We slightly modified the shape of qvib.
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Cro
ss s
ectio
n [
cm2 ]
10-2
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101
102
103
Electron energy [eV]
v4
v2
v1 v3
qa×100
qvib (4) F-
MURORAN INSTITUTE OF TECHNOLOGY
Dissociation qd (5)
For qd, we have some measured data and consider five kind of qd.(CF3, CF2, CF, CHF2 and CHF)
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Cro
ss s
ectio
n [
cm2 ]
10-2
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103
Electron energy [eV]
CF3
CHF2
CF2
CHFCF
Experiment Goto et al. (1994) Sugai et al. (1995) Motlagh et al. (1998)
MURORAN INSTITUTE OF TECHNOLOGY
Dissociation qd (5)
qd of CF and CF2 follows measured data reported by Sugai et al. (Contrib. Plasma Phys. 35 (1995) 415)
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Cro
ss s
ectio
n [
cm2 ]
10-2
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100
101
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103
Electron energy [eV]
CF2
Experiment Sugai et al. (1995)
CF
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Dissociation qd (5)
� CHF2 and CF3� Measured data (Motlagh et al.: J. Chem. Phys. 109 (1998) 432)� Calculated data (Morgan et al.: J. Phys. D, 90 (2001) 2009 )
� CHF� Measured data (Goto et al.: Jpn. J. Appl. Phys. 33 (1994) 3602)� Calculated data (Morgan et al.)
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Cro
ss s
ectio
n [
cm2 ]
10-2
10-1
100
101
102
103
Electron energy [eV]
CF3
CHF2
CHF
Experiment Goto et al. (1994) Motlagh et al. (1998)
Theoretical calculation
Morgan et al. (2001)
• The other three cross sections, we have measured data and also theoretically calculated data.
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Dissociation qd (5)
We estimated the shape of CF3, CHF2 and CHF, as shown in bold lines
� CHF2 and CF3� Measured data (Motlagh et al.: J. Chem. Phys. 109 (1998) 432)� Calculated data (Morgan et al.: J. Phys. D, 90 (2001) 2009 )
� CHF� Measured data (Goto et al.: Jpn. J. Appl. Phys. 33 (1994) 3602)� Calculated data (Morgan et al.)
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10-14
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Cro
ss s
ectio
n [
cm2 ]
10-2
10-1
100
101
102
103
Electron energy [eV]
CF3
CHF2
CHF
Experiment Goto et al. (1994) Motlagh et al. (1998)
Theoretical calculation
Morgan et al. (2001)
• The other three cross sections, we have measured data and also theoretically calculated data.
MURORAN INSTITUTE OF TECHNOLOGY
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10-14
10-13
Cro
ss s
ect
ion
[cm2 ]
10-2
10-1
100
101
102
103
Electron energy [eV]
HF+
C+ CHF
+
CH+
F+
H+
CF2+
CF+
CHF2+
Experiment Torres et al. (2002)
CF3+
qi (10)
Dissociative ionisation qi (10)
qi follows measured data by Torres et al. (J. Phys. B, 35 (2002) 2423).
MURORAN INSTITUTE OF TECHNOLOGY
Estimated set for CHF3
We calculate electron drift velocity, longitudinal diffusion coefficient and effective ionisation coefficient from the estimated set, and compare them with measured data.
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10-13
Cro
ss s
ectio
n [
cm2 ]
10-2
10-1
100
101
102
103
Electron energy [eV]
v4
v2
v1v3
qa (1)×100
qm
CF3
CHF2
CF2
CHF
CF
HF+
C+
CHF+
CH+
F+
H+
CF2+
CF+
CHF2+
CF3+qvib (4)
qi (10)
qd (5)
F-
MURORAN INSTITUTE OF TECHNOLOGY
W and NDL calculated using the estimated set
Electron drift velocity Longitudinal diffusion coefficient
W and NDL calculated from the estimated set (plotted as ) agree well with measured data in a wide range of E/N.
104
105
106
107
108
Ele
ctro
n d
rift v
elo
city
[c
m/s
]
10-1
100
101
102
103
E/N [Td]
Measurements Pulsed experiment (Wang et al. (1999)) Double-shutter method (Nakamura (2006))
Monte Carlo simulation (MCS) (Wm)
w/ Kushner's set w/ Bordage's set w/ Morgan's set w/ Nakamura's set w/ Voloshin's set w/ Present set
1020
2
4
6
810
21
2
4
6
810
22
2
4
6
810
23
Lo
ng
itud
inal
diff
usi
on
co
effic
ien
t ND
L
[cm
-1s-1
]10
02 3 4 5 6
101
2 3 4 5 6
102
2 3 4 5 6
103
E/N [Td]
Measurement Double-shutter method
(Nakamura (2006))MCS
w/ Kushner's set w/ Bordage's set w/ Morgan's set w/ Nakamura's set w/ Voloshin's set w/ Present set
MURORAN INSTITUTE OF TECHNOLOGY
(α−η)/N calculated using the estimated set
Also, calculated (α−η)/N using the estimated set (plotted as ) agree well with measured data.
200x10-18
150
100
50
0
Effe
ctiv
e io
nis
atio
n c
oef
ficie
nt
(α−η)
/ N
[c
m2 ]
3 4 5 6 7 8 9
102
2 3 4 5 6 7 8 9
103
E/N [Td]
Measurements Pulsed experiment (de Urquijo et al. (1999)) SST experiment (Nakamura (2006))
MCS
w/ Kushner's set w/ Bordage's set w/ Morgan's set w/ Nakamura's set w/ Voloshin's set w/ Present set
This result shows the validity of the estimated set.
MURORAN INSTITUTE OF TECHNOLOGY
Conclusions
�We evaluated the previously reported sets for CHF3.• For electron drift velocity W, the calculated values using Voloshin's set
agree well with measured data in a wide range of E/N.
• For longitudinal diffusion coefficient NDL, the calculated values usingNakamura's set agree well with measured data in a wide range of E/N.
• For effective ionisation coefficient (α−η)/N, the calculated values usingpreviously reported sets are close to measured data, but no calculatedvalues agree with measurements.
• This leads that the accurate set for CHF3 needs to be estimated.
� We estimated the set for CHF3, and the set is evaluated.• Electron drift velocity, longitudinal diffusion coefficient and effective
ionisation coefficient calculated using the estimated set agree well withmeasured data in a wide range of E/N.
• This confirms the validity of the estimated set.
MURORAN INSTITUTE OF TECHNOLOGY
Thank you very much for your attention.
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